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            <ul>
<li><a class="reference internal" href="#">Species distribution modeling</a><ul>
<li><a class="reference internal" href="#references">References</a></li>
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  <div class="sphx-glr-download-link-note admonition note">
<p class="admonition-title">Note</p>
<p>Click <a class="reference internal" href="#sphx-glr-download-auto-examples-applications-plot-species-distribution-modeling-py"><span class="std std-ref">here</span></a> to download the full example code or to run this example in your browser via Binder</p>
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<div class="sphx-glr-example-title section" id="species-distribution-modeling">
<span id="sphx-glr-auto-examples-applications-plot-species-distribution-modeling-py"></span><h1>Species distribution modeling<a class="headerlink" href="#species-distribution-modeling" title="Permalink to this headline">¶</a></h1>
<p>Modeling species’ geographic distributions is an important
problem in conservation biology. In this example we
model the geographic distribution of two south american
mammals given past observations and 14 environmental
variables. Since we have only positive examples (there are
no unsuccessful observations), we cast this problem as a
density estimation problem and use the <a class="reference internal" href="../../modules/generated/sklearn.svm.OneClassSVM.html#sklearn.svm.OneClassSVM" title="sklearn.svm.OneClassSVM"><code class="xref py py-class docutils literal notranslate"><span class="pre">sklearn.svm.OneClassSVM</span></code></a>
as our modeling tool. The dataset is provided by Phillips et. al. (2006).
If available, the example uses
<a class="reference external" href="https://matplotlib.org/basemap/">basemap</a>
to plot the coast lines and national boundaries of South America.</p>
<p>The two species are:</p>
<blockquote>
<div><ul class="simple">
<li><p><a class="reference external" href="http://www.iucnredlist.org/details/3038/0">“Bradypus variegatus”</a> ,
the Brown-throated Sloth.</p></li>
<li><p><a class="reference external" href="http://www.iucnredlist.org/details/13408/0">“Microryzomys minutus”</a> ,
also known as the Forest Small Rice Rat, a rodent that lives in Peru,
Colombia, Ecuador, Peru, and Venezuela.</p></li>
</ul>
</div></blockquote>
<div class="section" id="references">
<h2>References<a class="headerlink" href="#references" title="Permalink to this headline">¶</a></h2>
<blockquote>
<div><ul class="simple">
<li><p><a class="reference external" href="http://rob.schapire.net/papers/ecolmod.pdf">“Maximum entropy modeling of species geographic distributions”</a>
S. J. Phillips, R. P. Anderson, R. E. Schapire - Ecological Modelling,
190:231-259, 2006.</p></li>
</ul>
</div></blockquote>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="c1"># Authors: Peter Prettenhofer &lt;peter.prettenhofer@gmail.com&gt;</span>
<span class="c1">#          Jake Vanderplas &lt;vanderplas@astro.washington.edu&gt;</span>
<span class="c1">#</span>
<span class="c1"># License: BSD 3 clause</span>

<span class="kn">from</span> <span class="nn">time</span> <span class="kn">import</span> <span class="n">time</span>

<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>

<span class="kn">from</span> <span class="nn">sklearn.utils</span> <span class="kn">import</span> <span class="n">Bunch</span>
<span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <span class="n">fetch_species_distributions</span>
<span class="kn">from</span> <span class="nn">sklearn</span> <span class="kn">import</span> <span class="n">svm</span><span class="p">,</span> <span class="n">metrics</span>

<span class="c1"># if basemap is available, we&#39;ll use it.</span>
<span class="c1"># otherwise, we&#39;ll improvise later...</span>
<span class="k">try</span><span class="p">:</span>
    <span class="kn">from</span> <span class="nn">mpl_toolkits.basemap</span> <span class="kn">import</span> <span class="n">Basemap</span>
    <span class="n">basemap</span> <span class="o">=</span> <span class="kc">True</span>
<span class="k">except</span> <span class="ne">ImportError</span><span class="p">:</span>
    <span class="n">basemap</span> <span class="o">=</span> <span class="kc">False</span>

<span class="nb">print</span><span class="p">(</span><span class="vm">__doc__</span><span class="p">)</span>


<span class="k">def</span> <span class="nf">construct_grids</span><span class="p">(</span><span class="n">batch</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot;Construct the map grid from the batch object</span>

<span class="sd">    Parameters</span>
<span class="sd">    ----------</span>
<span class="sd">    batch : Batch object</span>
<span class="sd">        The object returned by :func:`fetch_species_distributions`</span>

<span class="sd">    Returns</span>
<span class="sd">    -------</span>
<span class="sd">    (xgrid, ygrid) : 1-D arrays</span>
<span class="sd">        The grid corresponding to the values in batch.coverages</span>
<span class="sd">    &quot;&quot;&quot;</span>
    <span class="c1"># x,y coordinates for corner cells</span>
    <span class="n">xmin</span> <span class="o">=</span> <span class="n">batch</span><span class="o">.</span><span class="n">x_left_lower_corner</span> <span class="o">+</span> <span class="n">batch</span><span class="o">.</span><span class="n">grid_size</span>
    <span class="n">xmax</span> <span class="o">=</span> <span class="n">xmin</span> <span class="o">+</span> <span class="p">(</span><span class="n">batch</span><span class="o">.</span><span class="n">Nx</span> <span class="o">*</span> <span class="n">batch</span><span class="o">.</span><span class="n">grid_size</span><span class="p">)</span>
    <span class="n">ymin</span> <span class="o">=</span> <span class="n">batch</span><span class="o">.</span><span class="n">y_left_lower_corner</span> <span class="o">+</span> <span class="n">batch</span><span class="o">.</span><span class="n">grid_size</span>
    <span class="n">ymax</span> <span class="o">=</span> <span class="n">ymin</span> <span class="o">+</span> <span class="p">(</span><span class="n">batch</span><span class="o">.</span><span class="n">Ny</span> <span class="o">*</span> <span class="n">batch</span><span class="o">.</span><span class="n">grid_size</span><span class="p">)</span>

    <span class="c1"># x coordinates of the grid cells</span>
    <span class="n">xgrid</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">xmin</span><span class="p">,</span> <span class="n">xmax</span><span class="p">,</span> <span class="n">batch</span><span class="o">.</span><span class="n">grid_size</span><span class="p">)</span>
    <span class="c1"># y coordinates of the grid cells</span>
    <span class="n">ygrid</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">ymin</span><span class="p">,</span> <span class="n">ymax</span><span class="p">,</span> <span class="n">batch</span><span class="o">.</span><span class="n">grid_size</span><span class="p">)</span>

    <span class="k">return</span> <span class="p">(</span><span class="n">xgrid</span><span class="p">,</span> <span class="n">ygrid</span><span class="p">)</span>


<span class="k">def</span> <span class="nf">create_species_bunch</span><span class="p">(</span><span class="n">species_name</span><span class="p">,</span> <span class="n">train</span><span class="p">,</span> <span class="n">test</span><span class="p">,</span> <span class="n">coverages</span><span class="p">,</span> <span class="n">xgrid</span><span class="p">,</span> <span class="n">ygrid</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot;Create a bunch with information about a particular organism</span>

<span class="sd">    This will use the test/train record arrays to extract the</span>
<span class="sd">    data specific to the given species name.</span>
<span class="sd">    &quot;&quot;&quot;</span>
    <span class="n">bunch</span> <span class="o">=</span> <span class="n">Bunch</span><span class="p">(</span><span class="n">name</span><span class="o">=</span><span class="s1">&#39; &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">species_name</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="s2">&quot;_&quot;</span><span class="p">)[:</span><span class="mi">2</span><span class="p">]))</span>
    <span class="n">species_name</span> <span class="o">=</span> <span class="n">species_name</span><span class="o">.</span><span class="n">encode</span><span class="p">(</span><span class="s1">&#39;ascii&#39;</span><span class="p">)</span>
    <span class="n">points</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">(</span><span class="n">test</span><span class="o">=</span><span class="n">test</span><span class="p">,</span> <span class="n">train</span><span class="o">=</span><span class="n">train</span><span class="p">)</span>

    <span class="k">for</span> <span class="n">label</span><span class="p">,</span> <span class="n">pts</span> <span class="ow">in</span> <span class="n">points</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
        <span class="c1"># choose points associated with the desired species</span>
        <span class="n">pts</span> <span class="o">=</span> <span class="n">pts</span><span class="p">[</span><span class="n">pts</span><span class="p">[</span><span class="s1">&#39;species&#39;</span><span class="p">]</span> <span class="o">==</span> <span class="n">species_name</span><span class="p">]</span>
        <span class="n">bunch</span><span class="p">[</span><span class="s1">&#39;pts_</span><span class="si">%s</span><span class="s1">&#39;</span> <span class="o">%</span> <span class="n">label</span><span class="p">]</span> <span class="o">=</span> <span class="n">pts</span>

        <span class="c1"># determine coverage values for each of the training &amp; testing points</span>
        <span class="n">ix</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">searchsorted</span><span class="p">(</span><span class="n">xgrid</span><span class="p">,</span> <span class="n">pts</span><span class="p">[</span><span class="s1">&#39;dd long&#39;</span><span class="p">])</span>
        <span class="n">iy</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">searchsorted</span><span class="p">(</span><span class="n">ygrid</span><span class="p">,</span> <span class="n">pts</span><span class="p">[</span><span class="s1">&#39;dd lat&#39;</span><span class="p">])</span>
        <span class="n">bunch</span><span class="p">[</span><span class="s1">&#39;cov_</span><span class="si">%s</span><span class="s1">&#39;</span> <span class="o">%</span> <span class="n">label</span><span class="p">]</span> <span class="o">=</span> <span class="n">coverages</span><span class="p">[:,</span> <span class="o">-</span><span class="n">iy</span><span class="p">,</span> <span class="n">ix</span><span class="p">]</span><span class="o">.</span><span class="n">T</span>

    <span class="k">return</span> <span class="n">bunch</span>


<span class="k">def</span> <span class="nf">plot_species_distribution</span><span class="p">(</span><span class="n">species</span><span class="o">=</span><span class="p">(</span><span class="s2">&quot;bradypus_variegatus_0&quot;</span><span class="p">,</span>
                                       <span class="s2">&quot;microryzomys_minutus_0&quot;</span><span class="p">)):</span>
    <span class="sd">&quot;&quot;&quot;</span>
<span class="sd">    Plot the species distribution.</span>
<span class="sd">    &quot;&quot;&quot;</span>
    <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">species</span><span class="p">)</span> <span class="o">&gt;</span> <span class="mi">2</span><span class="p">:</span>
        <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Note: when more than two species are provided,&quot;</span>
              <span class="s2">&quot; only the first two will be used&quot;</span><span class="p">)</span>

    <span class="n">t0</span> <span class="o">=</span> <span class="n">time</span><span class="p">()</span>

    <span class="c1"># Load the compressed data</span>
    <span class="n">data</span> <span class="o">=</span> <span class="n">fetch_species_distributions</span><span class="p">()</span>

    <span class="c1"># Set up the data grid</span>
    <span class="n">xgrid</span><span class="p">,</span> <span class="n">ygrid</span> <span class="o">=</span> <span class="n">construct_grids</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>

    <span class="c1"># The grid in x,y coordinates</span>
    <span class="n">X</span><span class="p">,</span> <span class="n">Y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span><span class="p">(</span><span class="n">xgrid</span><span class="p">,</span> <span class="n">ygrid</span><span class="p">[::</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>

    <span class="c1"># create a bunch for each species</span>
    <span class="n">BV_bunch</span> <span class="o">=</span> <span class="n">create_species_bunch</span><span class="p">(</span><span class="n">species</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span>
                                    <span class="n">data</span><span class="o">.</span><span class="n">train</span><span class="p">,</span> <span class="n">data</span><span class="o">.</span><span class="n">test</span><span class="p">,</span>
                                    <span class="n">data</span><span class="o">.</span><span class="n">coverages</span><span class="p">,</span> <span class="n">xgrid</span><span class="p">,</span> <span class="n">ygrid</span><span class="p">)</span>
    <span class="n">MM_bunch</span> <span class="o">=</span> <span class="n">create_species_bunch</span><span class="p">(</span><span class="n">species</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span>
                                    <span class="n">data</span><span class="o">.</span><span class="n">train</span><span class="p">,</span> <span class="n">data</span><span class="o">.</span><span class="n">test</span><span class="p">,</span>
                                    <span class="n">data</span><span class="o">.</span><span class="n">coverages</span><span class="p">,</span> <span class="n">xgrid</span><span class="p">,</span> <span class="n">ygrid</span><span class="p">)</span>

    <span class="c1"># background points (grid coordinates) for evaluation</span>
    <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">seed</span><span class="p">(</span><span class="mi">13</span><span class="p">)</span>
    <span class="n">background_points</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">c_</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="n">low</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">high</span><span class="o">=</span><span class="n">data</span><span class="o">.</span><span class="n">Ny</span><span class="p">,</span>
                                                <span class="n">size</span><span class="o">=</span><span class="mi">10000</span><span class="p">),</span>
                              <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="n">low</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">high</span><span class="o">=</span><span class="n">data</span><span class="o">.</span><span class="n">Nx</span><span class="p">,</span>
                                                <span class="n">size</span><span class="o">=</span><span class="mi">10000</span><span class="p">)]</span><span class="o">.</span><span class="n">T</span>

    <span class="c1"># We&#39;ll make use of the fact that coverages[6] has measurements at all</span>
    <span class="c1"># land points.  This will help us decide between land and water.</span>
    <span class="n">land_reference</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="n">coverages</span><span class="p">[</span><span class="mi">6</span><span class="p">]</span>

    <span class="c1"># Fit, predict, and plot for each species.</span>
    <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">species</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">([</span><span class="n">BV_bunch</span><span class="p">,</span> <span class="n">MM_bunch</span><span class="p">]):</span>
        <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;_&quot;</span> <span class="o">*</span> <span class="mi">80</span><span class="p">)</span>
        <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Modeling distribution of species &#39;</span><span class="si">%s</span><span class="s2">&#39;&quot;</span> <span class="o">%</span> <span class="n">species</span><span class="o">.</span><span class="n">name</span><span class="p">)</span>

        <span class="c1"># Standardize features</span>
        <span class="n">mean</span> <span class="o">=</span> <span class="n">species</span><span class="o">.</span><span class="n">cov_train</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
        <span class="n">std</span> <span class="o">=</span> <span class="n">species</span><span class="o">.</span><span class="n">cov_train</span><span class="o">.</span><span class="n">std</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
        <span class="n">train_cover_std</span> <span class="o">=</span> <span class="p">(</span><span class="n">species</span><span class="o">.</span><span class="n">cov_train</span> <span class="o">-</span> <span class="n">mean</span><span class="p">)</span> <span class="o">/</span> <span class="n">std</span>

        <span class="c1"># Fit OneClassSVM</span>
        <span class="nb">print</span><span class="p">(</span><span class="s2">&quot; - fit OneClassSVM ... &quot;</span><span class="p">,</span> <span class="n">end</span><span class="o">=</span><span class="s1">&#39;&#39;</span><span class="p">)</span>
        <span class="n">clf</span> <span class="o">=</span> <span class="n">svm</span><span class="o">.</span><span class="n">OneClassSVM</span><span class="p">(</span><span class="n">nu</span><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span> <span class="n">kernel</span><span class="o">=</span><span class="s2">&quot;rbf&quot;</span><span class="p">,</span> <span class="n">gamma</span><span class="o">=</span><span class="mf">0.5</span><span class="p">)</span>
        <span class="n">clf</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">train_cover_std</span><span class="p">)</span>
        <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;done.&quot;</span><span class="p">)</span>

        <span class="c1"># Plot map of South America</span>
        <span class="n">plt</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
        <span class="k">if</span> <span class="n">basemap</span><span class="p">:</span>
            <span class="nb">print</span><span class="p">(</span><span class="s2">&quot; - plot coastlines using basemap&quot;</span><span class="p">)</span>
            <span class="n">m</span> <span class="o">=</span> <span class="n">Basemap</span><span class="p">(</span><span class="n">projection</span><span class="o">=</span><span class="s1">&#39;cyl&#39;</span><span class="p">,</span> <span class="n">llcrnrlat</span><span class="o">=</span><span class="n">Y</span><span class="o">.</span><span class="n">min</span><span class="p">(),</span>
                        <span class="n">urcrnrlat</span><span class="o">=</span><span class="n">Y</span><span class="o">.</span><span class="n">max</span><span class="p">(),</span> <span class="n">llcrnrlon</span><span class="o">=</span><span class="n">X</span><span class="o">.</span><span class="n">min</span><span class="p">(),</span>
                        <span class="n">urcrnrlon</span><span class="o">=</span><span class="n">X</span><span class="o">.</span><span class="n">max</span><span class="p">(),</span> <span class="n">resolution</span><span class="o">=</span><span class="s1">&#39;c&#39;</span><span class="p">)</span>
            <span class="n">m</span><span class="o">.</span><span class="n">drawcoastlines</span><span class="p">()</span>
            <span class="n">m</span><span class="o">.</span><span class="n">drawcountries</span><span class="p">()</span>
        <span class="k">else</span><span class="p">:</span>
            <span class="nb">print</span><span class="p">(</span><span class="s2">&quot; - plot coastlines from coverage&quot;</span><span class="p">)</span>
            <span class="n">plt</span><span class="o">.</span><span class="n">contour</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">land_reference</span><span class="p">,</span>
                        <span class="n">levels</span><span class="o">=</span><span class="p">[</span><span class="o">-</span><span class="mi">9998</span><span class="p">],</span> <span class="n">colors</span><span class="o">=</span><span class="s2">&quot;k&quot;</span><span class="p">,</span>
                        <span class="n">linestyles</span><span class="o">=</span><span class="s2">&quot;solid&quot;</span><span class="p">)</span>
            <span class="n">plt</span><span class="o">.</span><span class="n">xticks</span><span class="p">([])</span>
            <span class="n">plt</span><span class="o">.</span><span class="n">yticks</span><span class="p">([])</span>

        <span class="nb">print</span><span class="p">(</span><span class="s2">&quot; - predict species distribution&quot;</span><span class="p">)</span>

        <span class="c1"># Predict species distribution using the training data</span>
        <span class="n">Z</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">data</span><span class="o">.</span><span class="n">Ny</span><span class="p">,</span> <span class="n">data</span><span class="o">.</span><span class="n">Nx</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span>

        <span class="c1"># We&#39;ll predict only for the land points.</span>
        <span class="n">idx</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">land_reference</span> <span class="o">&gt;</span> <span class="o">-</span><span class="mi">9999</span><span class="p">)</span>
        <span class="n">coverages_land</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="n">coverages</span><span class="p">[:,</span> <span class="n">idx</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">idx</span><span class="p">[</span><span class="mi">1</span><span class="p">]]</span><span class="o">.</span><span class="n">T</span>

        <span class="n">pred</span> <span class="o">=</span> <span class="n">clf</span><span class="o">.</span><span class="n">decision_function</span><span class="p">((</span><span class="n">coverages_land</span> <span class="o">-</span> <span class="n">mean</span><span class="p">)</span> <span class="o">/</span> <span class="n">std</span><span class="p">)</span>
        <span class="n">Z</span> <span class="o">*=</span> <span class="n">pred</span><span class="o">.</span><span class="n">min</span><span class="p">()</span>
        <span class="n">Z</span><span class="p">[</span><span class="n">idx</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">idx</span><span class="p">[</span><span class="mi">1</span><span class="p">]]</span> <span class="o">=</span> <span class="n">pred</span>

        <span class="n">levels</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">Z</span><span class="o">.</span><span class="n">min</span><span class="p">(),</span> <span class="n">Z</span><span class="o">.</span><span class="n">max</span><span class="p">(),</span> <span class="mi">25</span><span class="p">)</span>
        <span class="n">Z</span><span class="p">[</span><span class="n">land_reference</span> <span class="o">==</span> <span class="o">-</span><span class="mi">9999</span><span class="p">]</span> <span class="o">=</span> <span class="o">-</span><span class="mi">9999</span>

        <span class="c1"># plot contours of the prediction</span>
        <span class="n">plt</span><span class="o">.</span><span class="n">contourf</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">Z</span><span class="p">,</span> <span class="n">levels</span><span class="o">=</span><span class="n">levels</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">Reds</span><span class="p">)</span>
        <span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span><span class="p">(</span><span class="nb">format</span><span class="o">=</span><span class="s1">&#39;</span><span class="si">%.2f</span><span class="s1">&#39;</span><span class="p">)</span>

        <span class="c1"># scatter training/testing points</span>
        <span class="n">plt</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">species</span><span class="o">.</span><span class="n">pts_train</span><span class="p">[</span><span class="s1">&#39;dd long&#39;</span><span class="p">],</span> <span class="n">species</span><span class="o">.</span><span class="n">pts_train</span><span class="p">[</span><span class="s1">&#39;dd lat&#39;</span><span class="p">],</span>
                    <span class="n">s</span><span class="o">=</span><span class="mi">2</span> <span class="o">**</span> <span class="mi">2</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="s1">&#39;black&#39;</span><span class="p">,</span>
                    <span class="n">marker</span><span class="o">=</span><span class="s1">&#39;^&#39;</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">&#39;train&#39;</span><span class="p">)</span>
        <span class="n">plt</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">species</span><span class="o">.</span><span class="n">pts_test</span><span class="p">[</span><span class="s1">&#39;dd long&#39;</span><span class="p">],</span> <span class="n">species</span><span class="o">.</span><span class="n">pts_test</span><span class="p">[</span><span class="s1">&#39;dd lat&#39;</span><span class="p">],</span>
                    <span class="n">s</span><span class="o">=</span><span class="mi">2</span> <span class="o">**</span> <span class="mi">2</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="s1">&#39;black&#39;</span><span class="p">,</span>
                    <span class="n">marker</span><span class="o">=</span><span class="s1">&#39;x&#39;</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">&#39;test&#39;</span><span class="p">)</span>
        <span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
        <span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="n">species</span><span class="o">.</span><span class="n">name</span><span class="p">)</span>
        <span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s1">&#39;equal&#39;</span><span class="p">)</span>

        <span class="c1"># Compute AUC with regards to background points</span>
        <span class="n">pred_background</span> <span class="o">=</span> <span class="n">Z</span><span class="p">[</span><span class="n">background_points</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">background_points</span><span class="p">[</span><span class="mi">1</span><span class="p">]]</span>
        <span class="n">pred_test</span> <span class="o">=</span> <span class="n">clf</span><span class="o">.</span><span class="n">decision_function</span><span class="p">((</span><span class="n">species</span><span class="o">.</span><span class="n">cov_test</span> <span class="o">-</span> <span class="n">mean</span><span class="p">)</span> <span class="o">/</span> <span class="n">std</span><span class="p">)</span>
        <span class="n">scores</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">r_</span><span class="p">[</span><span class="n">pred_test</span><span class="p">,</span> <span class="n">pred_background</span><span class="p">]</span>
        <span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">r_</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">pred_test</span><span class="o">.</span><span class="n">shape</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">pred_background</span><span class="o">.</span><span class="n">shape</span><span class="p">)]</span>
        <span class="n">fpr</span><span class="p">,</span> <span class="n">tpr</span><span class="p">,</span> <span class="n">thresholds</span> <span class="o">=</span> <span class="n">metrics</span><span class="o">.</span><span class="n">roc_curve</span><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="n">scores</span><span class="p">)</span>
        <span class="n">roc_auc</span> <span class="o">=</span> <span class="n">metrics</span><span class="o">.</span><span class="n">auc</span><span class="p">(</span><span class="n">fpr</span><span class="p">,</span> <span class="n">tpr</span><span class="p">)</span>
        <span class="n">plt</span><span class="o">.</span><span class="n">text</span><span class="p">(</span><span class="o">-</span><span class="mi">35</span><span class="p">,</span> <span class="o">-</span><span class="mi">70</span><span class="p">,</span> <span class="s2">&quot;AUC: </span><span class="si">%.3f</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="n">roc_auc</span><span class="p">,</span> <span class="n">ha</span><span class="o">=</span><span class="s2">&quot;right&quot;</span><span class="p">)</span>
        <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2"> Area under the ROC curve : </span><span class="si">%f</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="n">roc_auc</span><span class="p">)</span>

    <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">time elapsed: </span><span class="si">%.2f</span><span class="s2">s&quot;</span> <span class="o">%</span> <span class="p">(</span><span class="n">time</span><span class="p">()</span> <span class="o">-</span> <span class="n">t0</span><span class="p">))</span>


<span class="n">plot_species_distribution</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
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        var top = target.getBoundingClientRect().top;
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    };

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    var navBarToggler = document.getElementById("sk-navbar-toggler");
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        }
        if (lastScrollTop > 2 && (prevScrollpos <= lastScrollTop) || hashTargetOnTop()){
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        } else {
            showNavBar()
        }
        prevScrollpos = lastScrollTop;
    };

    /*** high preformance scroll event listener***/
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        window.webkitRequestAnimationFrame ||
        window.mozRequestAnimationFrame ||
        window.msRequestAnimationFrame ||
        window.oRequestAnimationFrame;
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    if (raf) {
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    function loop() {
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            lastScrollTop = scrollTop;
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            raf(loop);
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